I'm reviewing a logic text for an academic publisher. The author strains to explain the concept of validity, using awkward terms like "hypothetical truth" and "actual truth." It's really not that hard. Validity may be explained as follows:
A valid argument is one in which the truth of the premises is incompatible with the falsity of the conclusion.
Three things follow from this definition:
- If a particular valid argument has true premises, then it cannot, and hence does not, have a false conclusion.
- If a particular valid argument has a false conclusion, then it cannot, and hence does not, have true premises.
- If a particular argument has true premises and a false conclusion, then it cannot be, and hence is not, valid.
Validity is a relation between the premises and the conclusion of an argument. Soundness, by contrast, is a (compound) property of an argument. An argument is sound if and only if (1) it is valid and (2) its premises are true. A given argument may lack both of these properties. That is, it may be invalid and have one or more false premises. There is no word for this special argument other than "unsound." All we can say is that the argument is unsound twice over, or in two different ways, or that it is doubly unsound.
If you're constructing an argument, try to make it sound, for it will then have a true conclusion. (Do you see why?) If you're criticizing an argument, try to show that it is doubly unsound. There are no sweeter words in the English language than, "At least one of your premises is false; but even if all of your premises were true, your conclusion wouldn't follow from them." I tell my students to be relentless in their criticisms. There is no such thing as "piling on" when it comes to argumentation. We expect a prosecutor to bring all available charges against a given defendant. A critic should bring all available charges against a given argument. If one of your charges turns out to be false, you may fall back on the other or others. It's always good to have a fall-back position.
